Not my field either, but I was curious so spent several hours with various resources at hand. I very much agree with David, these stone head clubs actually used in various Plains tribes, were secured with rawhide which was wetted then when dried tightly secured the stone head. Sinew would not have been sufficient.

It also seems that these stone clubs became rather obsolete with steel tomahawks and especially firearms. Some later versions were used ceremonially, but with far larger stone heads and notable decoration.

The small size of this piece makes me wonder if it might have been a 'coup stick', many of which did have a small stone head. It sees that 'counting coup' was a distinguished feat of bravery which involved either touching a fallen enemy with the coup stick in the heat of battle or an active enemy without any intent of wounding or killing him, then rushing away.
There seem to be various interpretations of this according to tribes etc. which in some cases called for notching or embellishing the stick, but more complex than can be described at this point.